Scores of Palestinians and more than a dozen Israeli soldiers died in a day of heavy fighting in Gaza, as Israel's prime minister Benjamin Netanyahu said there was "very strong" international support for his military's actions.

Officials in Gaza say more than 80 people during an Israeli assault on the neighbourhood of Shejaiya, in what some locals say is the heaviest fighting they have seen since 1967's Six-Day War.

Thirteen Israeli soldiers were killed, with a total of 18 now dead since the ground invasion began. Hamas is also claiming to have captured an Israeli soldier.

More than 400 Palestinians have now died in the current unrest and the Palestinian Authority says the attack on Shejaiya was a "massacre".

Israel says scores of Hamas fighters have been killed.

Correspondent Matt Brown in Gaza

During a brief ceasefire today brokered by the Red Cross, bodies were being pulled from the rubble - there were dead women and children in the streets.

People were walking through Shejaiya crying and injured - they were flooding into the main hospital in Gaza city. Medics say around half of the killed were women, children and elderly.

Airstrikes had reduced houses to rubble and there were a lot of other signs of conflict, like mortar strikes on the ground that had peppered walls of houses with shrapnel and punched through into lounge rooms, bedrooms and the like. It was a terrible, terrible scene.

Israel says Shejaiya is a neighbourhood that was used to fire rockets into Israel. It also says that Hamas had command posts there, that it had tunnels there.

There was an airstrike on a Hamas leader's house, which did kill him and members of his family.

And Hamas has actually said that they did fight in Shejaiya. They said that they used roadside bombs, IEDs, and also landmines - as well as obviously small arms fire and other sorts of weapons against the invading Israeli forces.

Residents inside Shejaiya say hundreds of shells were fired into the neighbourhood during an 18-hour period.

Israel says its operation was aimed at a Hamas leader and at Hamas rocket sites and tunnels in the area.

Hamas medical officials say around half the Palestinians who died were women, children and the elderly.

United Nations secretary-general Ban Ki-moon and US secretary of state John Kerry are in the region to try to arrange a ceasefire.

In a conversation caught on an open microphone before a Fox News interview, Mr Kerry was heard apparently expressing concern over the deaths of civilians in Gaza, saying: "It's a hell of a pinpoint operation. It's a hell of a pinpoint operation."

The UN Security Council later expressed serious concern at the escalation of the conflict and the number of casualties.

"The members of the Security Council called for an immediate cessation of hostilities," Rwandan UN ambassador Eugene Gasana said.

While Washington says Israel has a right to defend itself from rocket attacks launched out of Gaza, American diplomats have called on the Israelis to restrict themselves to a precise operation in the ground campaign, which was launched on Thursday.

Mr Netanyahu said Israel won "international legitimacy" for its military operation in Gaza after it accepted an Egyptian truce proposal on July 15 which was shunned by Hamas.

"We are carrying out a complex, deep, intensive activity inside the Gaza Strip and there is world support for this ... very strong support within the international community for the activity that the IDF is doing," Mr Netanyahu said at a press conference in the defence ministry in Tel Aviv.

"As a democratic state, Israel is using the legitimate tools of self-defence to try and harm those who are firing rockets at us. I think this distinction is clear to most world leaders."

Palestinian president Mahmoud Abbas has accused Israel of carrying out a massacre and declared three days of mourning.

"I am calling for an urgent session tonight of the UN Security Council," he said in a televised speech from the Qatari capital Doha.

"The situation is intolerable," he said, describing the Israeli attacks as "crimes against humanity".

Despite the UN's strong stance on ending the violence, Middle East analyst Aaron David Miller says the calls for ceasefire may not make a huge difference.

"[The UN Security Council meeting] doesn't really matter. The UN Security Council is not in a position to impose a ceasefire and I think this is going to have to be handled regionally," Dr Miller told ABC's The World Today.

"Qataris are going to have to be involved, the Egyptians, the Israelis, the United States to some degree, maybe the Turks."

US president Barack Obama spoke by telephone to Mr Netanyahu for the second time in three days overnight.

He told him Israel has the right to defend itself and he reiterated US condemnation of attacks by Hamas against Israel.

"The president also raised serious concern about the growing number of casualties, including increasing Palestinian civilian deaths in Gaza and the loss of Israeli soldiers," the White House said in a statement describing the conversation

Although Mr Netanyahu said the military's ground campaign would expand as much as necessary to destroy a network of cross-border tunnels used by militants to stage attacks inside Israel, defence minister Moshe Yaalon suggested it could be over within days.

"My assessment is that in another two or three days, the lion's share of the tunnels, from our perspective, will be destroyed," he said at the same press conference.

Israeli military said it had urged all residents of Shejaiya to leave the area two days ago, accusing Hamas militants of firing 140 rockets from the area since July 8, and using civilians as human shields.

Hamas has told residents to stay put and many locals say they have nowhere to go.

The largest UN agency in Gaza, United Relations Relief and Works Agency (UNRWA), said about 61,500 people had sought refuge in its buildings - more than in any previous conflict in the region between Israel and Islamist militants.

The enclave's borders with both Israel and Egypt are sealed off, meaning that people can only move around within the narrow confines of Gaza.

Israel says more than 1,700 rockets have been fired out of Gaza during this month's fighting with between 3,000 and 4,000 destroyed in military strikes - together almost half of the militants' original estimated arsenal.

Hamas says it is continuously replenishing its stock of weapons and is ready for a prolonged conflict.

The Israeli death toll has been kept low due to the rockets' relative inaccuracy, a network of air raid sirens and shelters, and the Iron Dome rocket interceptor's 90 per cent success rate.